The generic pair conjecture for dependent finite diagrams

TL;DR

This paper extends Shelah's generic pair conjecture from first order theories to finite diagrams, utilizing homogeneous models instead of saturated models, thereby broadening its applicability.

Contribution

It introduces a generalization of the generic pair conjecture to finite diagrams using homogeneous models, expanding the scope of the original theorem.

Findings

Proves the generic pair conjecture for finite diagrams.

Demonstrates the effectiveness of homogeneous models in this context.

Broadens the applicability of Shelah's theorem.

Abstract

This paper generalizes Shelah's generic pair conjecture (now theorem) for the measurable cardinal case from first order theories to finite diagrams. We use homogeneous models in the place of saturated models.